A common approach utilized in advanced industrial process control is Model-based Predictive Control, also known as “MPC”. MPC typically involves the use of a controller that utilizes a mathematical model of the process to predict the future behavior of the control system and formulate a control problem as a constrained optimization. The accuracy of the internal process model is crucial to control performance.
Control problems associated with MPC controllers are generally formulated as parametric quadratic programming (QP) problems. In standard industrial MPC applications, the sampling periods are typically on the order of seconds and minutes. Such sampling periods are sufficient for solving the QP problems utilizing, for example, a standard personal computer.
MPC is becoming increasingly popular in embedded process control applications such as, for example, automotive and aircraft control systems. In such control applications, the sampling frequencies are higher and computational resources such as, CPU and memory, are limited. Hence, a need exists for a fast and tailored QP solver for embedded applications with limited CPU and memory in order to utilize the MPC control approach under such conditions.
Most prior art approaches for solving the QP optimization problems utilize an active-set approach or an interior point approach. Such prior art approaches are sufficiently fast for process control applications running on the standard personal computers, but are not directly applicable for fast sampling control applications that run on embedded platforms. Multi-parametric quadratic programming (MPQP) solvers that include an off-line part and an on-line part can be alternatively employed for solving the control problems in the embedded applications. The MPQP can be solved by using an explicit approach based on the active-set approach in which the space of a parameter vector is divided into a number of sub-spaces/regions. Such regions are further stored into a memory for the on-line phase.
The online phase of the MPQP includes an algorithm for searching the region for a measured parameter vector and the algorithm is periodically executed in each sampling period. Such an approach can be employed for very small control problems only due to exponential growth of memory requirements. The number of computations involved in such complete enumeration strategies grows rapidly with the dimension sizes and length of the horizon, making the strategies slow to run and unsuitable for real time control of complex processes by using embedded platform (e.g. ECU for automotive applications).
Based on the foregoing, it is believed that a need exists for an improved system and method for solving a quadratic programming optimization problem using a semi-explicit QP solver, as described in greater detail herein.